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Optimal portfolios for DC pension plans under a CEV model

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  • Gao, Jianwei
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    Abstract

    This paper studies the portfolio optimization problem for an investor who seeks to maximize the expected utility of the terminal wealth in a DC pension plan. We focus on a constant elasticity of variance (CEV) model to describe the stock price dynamics, which is an extension of geometric Brownian motion. By applying stochastic optimal control, power transform and variable change technique, we derive the explicit solutions for the CRRA and CARA utility functions, respectively. Each solution consists of a moving Merton strategy and a correction factor. The moving Merton strategy is similar to the result of Devolder et al. [Devolder, P., Bosch, P.M., Dominguez F.I., 2003. Stochastic optimal control of annunity contracts. Insurance: Math. Econom. 33, 227-238], whereas it has an updated instantaneous volatility at the current time. The correction factor denotes a supplement term to hedge the volatility risk. In order to have a better understanding of the impact of the correction factor on the optimal strategy, we analyze the property of the correction factor. Finally, we present a numerical simulation to illustrate the properties and sensitivities of the correction factor and the optimal strategy.

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    File URL: http://www.sciencedirect.com/science/article/B6V8N-4VJBTJY-1/2/ca20b33833e8f0798913dc1f53881378
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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 44 (2009)
    Issue (Month): 3 (June)
    Pages: 479-490

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    Handle: RePEc:eee:insuma:v:44:y:2009:i:3:p:479-490

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Defined contribution pension plan Stochastic optimal control CEV model HJB equation Optimal portfolios;

    References

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    Citations

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    Cited by:
    1. Yao, Haixiang & Lai, Yongzeng & Ma, Qinghua & Jian, Minjie, 2014. "Asset allocation for a DC pension fund with stochastic income and mortality risk: A multi-period mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 84-92.
    2. Yao, Haixiang & Yang, Zhou & Chen, Ping, 2013. "Markowitz’s mean–variance defined contribution pension fund management under inflation: A continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 851-863.
    3. Gu, Mengdi & Yang, Yipeng & Li, Shoude & Zhang, Jingyi, 2010. "Constant elasticity of variance model for proportional reinsurance and investment strategies," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 580-587, June.
    4. Zhao, Hui & Rong, Ximin, 2012. "Portfolio selection problem with multiple risky assets under the constant elasticity of variance model," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 179-190.
    5. Gu, Ailing & Guo, Xianping & Li, Zhongfei & Zeng, Yan, 2012. "Optimal control of excess-of-loss reinsurance and investment for insurers under a CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 674-684.

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